5. Figs. a, cases 3 and 4, same table, represent simple beams suppofted at their ends, the first bearing a concentrated load P at the and the second a uniform load W. Figs.
are the corresponding shear diagrams. Take P and W equal to 1,000 pounds, and satisfy yourself that they are correct.
39. Maximum Shear. It is sometimes desirable to know the greatest or maximum value of the shear in a given case. This value can always be found with certainty by constructing the shear diagram, from which the maximum value of the shear is evident at a glance. In any case it can most readily be computed if one knows the section for which the shear is a maximum. The stu dent should examine all the shear diagrams in the preceding articles and those that he has drawn, and see that 1. in cantilevers fixed in a wall, the maximum, shear occurs at the wall.
2. In simple beams, the maximum shear occurs at a sec tion next to one of the supports.
By the use of these propositions one can determine the value of the maximum shear without constructing the whole shear diagram. Thus, it is easily seen (referring to the diagrams, page 55) that for a • Cantilever, end load P, maximum shear=P " , uniform load W, " .‘
Simple beam, middle load P, " (C " " , uniform " W, "V. Bending Moment. By bending moment at (or for) a section of a loaded beam, is meant the algebraic sum of the mo ments of all the loads (including weight of beam) and reactions to the left or right of the section with respect to any point in the section.
Rule of Signs. We follow the rule of signs previously stated (Art. 29) that the moment of a force which tends to pro duce clockwise rotation is plus, and that of a force which tends to produce counter-clockwise rotation is minus; but in order to get the same sign for the bending moment whether computed from the right or left, we change the sign of the sum of the moments when computed from the loads and reactions on the right. Thus for section a, Fig. 8, the algebraic sums of the moments of the forces are: when computed from tne left, —1,000X 5+3,000X foot-pounds; and when computed from the right,